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    <div class="caldb">

      <h1>ATCA Calibrator Database v3</h1>

      <div class="backToFront"><a href="calibrator_database.html">Back to front page</a></div>

      <br><br><br><h1>Documentation</h1>

      <div class="documentation-section">
	<a name="introduction">&nbsp;</a>
	<h2>Introduction</h2>
	<div>
	  <br>
	  Version 3 of the ATCA calibrator database represents a number of major
	  improvements, meant to improve the accuracy and reliability of the
	  data it presents. This documentation describes:
	  <ul>
	    <li>the measurement process that produces the information contained
	      in the calibrator database,</li>
	    <li>how to use the web interface to find the information you require,</li>
	    <li>how to interpret the numbers and graphs presented by the web
	      interface.</li>
	  </ul>
	  This documentation was last updated on 2014-Jan-21.
	</div>
      </div>

      <div class="documentation-section">
	<a name="measurement-process">&nbsp;</a>
	<h2>The Measurement Process</h2>
	<div>
	  <a name="measurement-process-loading-the-data">&nbsp;</a>
	  <h3>Loading the data</h3>
	  <div>
	    Loading the data is done manually, to screen out RPFITS files that
	    have calibration data in them (data during a dcal, pcal or acal for
	    example). If these data are mixed in with useful data then the
	    calibration data is manually flagged as bad.
	  </div>
	  <div>
	    The atlod step is done the same way for every band. For CABB data:
	    <code>
	      atlod "in=*.C007" options=birdie,rfiflag,noauto,xycorr,opcorr nopcorr=32 out=c007.uv
	    </code>
	    This command flags out all the frequency ranges that are commonly
	    affected by bad RFI, discards any autocorrelation data, corrects
	    for phase offsets between the X and Y polarisations on each antenna
	    and compensates for atmospheric opacity in 32 discrete bins across
	    each 2 GHz band. We do the opacity correction on such a fine scale
	    because in certain areas of the band (at high frequencies, and near
	    water lines for example), the opacity can change very quickly as
	    a function of frequency. Correcting opacity in this way will make
	    it less likely that our bandpasses will have curvature caused by
	    atmospheric effects later in our reduction.
	  </div>
	  <div>
	    For pre-CABB data:
	    <code>
	      atlod "in=*.C007" options=birdie,reweight,noauto,xycorr,nocacal,opcorr \<br>
	        nopcorr=2 out=c007.uv
	    </code>
	    This makes the opacity correction happen at the same resolution (64 MHz)
	    as for the CABB data, and does some pre-CABB correlator reweighting to
	    get rid of Gibbs ringing.
	  </div>
	  <div>
	    If the observations in this epoch are made in the 3mm band, we now
	    need to interpolate the system temperatures derived at each paddle
	    scan; we do this with atfix:
	    <code>
	      atfix vis=c007.uv out=c007a.uv tsyscal=interpolate<br>
	    </code>
	  </div>
	  <div>
	    We now split the data into sources, and deal with each band that
	    was observed separately, by using directories that are named for
	    the band. Except at 16cm, this means that there will be two
	    separate frequencies, usually separated by 2 GHz or more, in
	    each directory.
	  </div>
	</div> <!-- Loading the data -->
	<div>
	  <a name="measurement-process-bandpass-flux-calibration">&nbsp;</a>
	  <h3>Bandpass and flux calibration</h3>
	  <div>
	    There are two distinctly different schemes for bandpass calibration.
	    In the 16cm and 4cm bands, where the ATCA flux calibrator 1934-638
	    is bright enough to act as the bandpass calibrator, bandpass
	    calibration is done simply by running mfcal on its dataset at each
	    band frequency. For example, if we were reducing data at 16cm:
	    <code>
	      mfcal vis=1934-638.2100 interval=0.1
	    </code>
	    We use an interval of 0.1 minutes for the time-dependent gain
	    solution so that short-term variations do not get transferred
	    into the bandpass solution.
	  </div>
	  <div>
	    We then do further calibration with gpcal:
	    <code>
	      gpcal vis=1934-638.2100 interval=0.1 options=xyvary nfbin=2
	    </code>
	  </div>
	  <div>
	    We now do some automatic flagging using the AOFlagger algorithm
	    in pgflag:
	    <code>
	      pgflag vis=1934-638.2100 stokes=xx,yy command=&lt;b<br>
	      pgflag vis=1934-638.2100 stokes=yy,xx command=&lt;b
	    </code>
	  </div>
	  <div>
	    With flagging done, we delete all the calibration tables and
	    redo the exact same calibration commands as before, after which
	    we consider the flux and bandpass calibration to be done.
	  </div>
	  <div>
	    In higher frequency bands where the flux calibrator cannot
	    be used as the bandpass calibrator, either because it is too
	    faint (as in the case of 1934-638 in the mm bands) or too
	    large (as for Uranus), we need to use a more intricate calibration
	    scheme.
	  </div>
	  <div>
	    We begin by choosing a very bright calibrator from the list of
	    those observed during the epoch. Usually this is one of the
	    usual array setup calibrators, like 0537-441, 1253-055 or 1921-293
	    for example. We do the initial bandpass calibration as before:
	    <code>
	      mfcal vis=1921-293.17000 interval=0.1<br>
	      mfcal vis=1921-293.19000 interval=0.1
	    </code>
	    The problem that arises here though is that because there is no
	    definitive apriori information about the brightness and spectral
	    behaviour of the bandpass calibrator, the bandpass solution will
	    be wrong. Miriad assumes that the bandpass calibrator has a
	    flat-spectrum (the same flux density in each frequency channel),
	    which is likely to be incorrect for almost all calibrators.
	  </div>
	  <div>
	    Let's look at just how wrong this is. We do this using the new
	    Miriad task written especially for the v3 calibrator database,
	    uvfmeas. We can look at the spectral behaviour of the bandpass
	    calibrator over the observed frequency range.
	    <code>
	      uvfmeas vis=1921-293.1[79]000 stokes=i order=1 options=plotvec,log device=/xs
	    </code>
	  </div>
	  <img class="needs-border" src="1921-293.bandpassonly.png">
	  <div>
	    The bandpass calibration seems to have worked pretty well, since
	    the flux density in each band is constant over frequency, with
	    only small deviations. But the source is unlikely to be
	    actually flat-spectrum, as evidenced by the observation that the
	    flux density in each band is significantly different.
	  </div>
	  <div>
	    We thus have to determine the bandpass calibrator's spectral
	    behaviour and flux density. To do this we copy the the solution
	    we have just made to the flux calibrator to determine how
	    wrong it is. But the way this is done is different depending on
	    whether the flux calibrator is 1934-638 or Uranus. We deal with
	    the case of 1934-638 first.
	  </div>
	  <div>
	    The first step here is to do a further calibration with gpcal:
	    <code>
	      gpcal vis=1921-293.17000 interval=0.1 options=xyvary nfbin=2<br>
	      gpcal vis=1921-293.19000 interval=0.1 options=xyvary nfbin=2
	    </code>
	    And then copy these solutions to 1934-638:
	    <code>
	      gpcopy vis=1921-293.17000 out=1934-638.17000<br>
	      gpcopy vis=1921-293.19000 out=1934-638.19000
	    </code>
	    And then calibrate 1934-638 with gpcal:
	    <code>
	      gpcal vis=1934-638.17000 interval=0.1 options=xyvary nfbin=2<br>
	      gpcal vis=1934-638.19000 interval=0.1 options=xyvary nfbin=2
	    </code>
	    It is at this point that automatic flagging may be done on both
	    the bandpass and flux calibrators, but in most cases very little
	    flagging is required, and this step can usually be omitted.
	  </div>
	  <div>
	    Because we have solved for time-varying gains in two bins
	    across the band, gpcal can deal with both absolute scaling
	    of flux density, and with a slope correction due to the
	    error built into the bandpass solution:
	    <code>
	      gpboot vis=1921-293.17000 cal=1934-638.17000<br>
	      gpboot vis=1921-293.19000 cal=1934-638.19000
	    </code>
	  </div>
	  <div>
	    At this point we use uvfmeas to examine the spectrum of the
	    bandpass calibrator in the same way as before.
	  </div>
	  <img class="needs-border" src="1921-293.fluxcalr1.png">
	  <div>
	    Already this looks like a very large improvement, as the bands
	    almost join smoothly to each other; recall that the reduction
	    of the bands have been completely independent. However the
	    agreement between the bands is not perfect, and the bandpass
	    function itself is still incorrect.
	  </div>
	  <div>
	    On the plot above that uvfmeas generated, there is a red line;
	    this is the least-squares linear fit to $\log {\rm S} / \log\nu$.
	    On this occasion, the line of best fit is
	    <div class="equation">
	      $\log({\rm S} / 1 {\rm\,Jy}) = 1.685 - 0.3711\log(\nu / 1 {\rm\,GHz}),$
	    </div>
	    and there is an RMS scatter of 13.85 mJy of the measured flux densities
	    around this fit line. This would suggest that this fit is accurate to
	    1%, although there could still be uncertainty in the absolute flux
	    scaling. Investigations of absolute calibration accuracy was done with
	    simulations, and in that case it was possible to get better than 1%
	    accuracy on the bandpass calibrator's flux density using this method,
	    even if the fit made to each band separately could be in error by as
	    much as 10%.
	  </div>
	  <div>
	    To correct the bandpass function we go back to mfcal and input the
	    now known flux density model for the bandpass calibrator:
	    <code>
	      mfcal vis=1921-293.17000 interval=0.1 flux=16.9286,17.0,-0.3711<br>
	      mfcal vis=1921-293.19000 interval=0.1 flux=16.9286,17.0,-0.3711
	    </code>
	    Here, the flux specification is taken directly from the output of
	    uvfmeas with the mfflux option given.
	  </div>
	  <div>
	    We can now redo the flux calibration with 1934-638 as before.
	    After this, the best fit changes to:
	    <div class="equation">
	      $\log({\rm S} / 1 {\rm\,Jy}) = 1.685 - 0.3713\log(\nu / 1 {\rm\,GHz}),$
	    </div>
	    and the RMS scatter is decreased to 13.33 mJy. This of course is
	    not a large improvement, but simulations indicate that doing this
	    significantly improves the accuracy of flux density measurements for 
	    the other sources that the bandpass calibration is applied to.
	  </div>
	  <div>
	    If the flux calibrator is Uranus, then the procedure is slightly
	    different. We start the procedure in a similar way, by doing the mfcal
	    and gpcal steps on the bandpass calibrator:
	    <code>
	      mfcal vis=1921-293.33000 interval=0.1<br>
	      mfcal vis=1921-293.35000 interval=0.1<br>
	      gpcal vis=1921-293.33000 interval=0.1 options=xyvary<br>
	      gpcal vis=1921-293.35000 interval=0.1 options=xyvary
	    </code>
	    Then we copy the gain and bandpass solutions to the flux calibrator:
	    <code>
	      gpcopy vis=1921-293.33000 out=uranus.33000<br>
	      gpcopy vis=1921-293.35000 out=uranus.35000
	    </code>
	    And use mfboot to correct the bandpass and flux scale:
	    <code>
	      mfboot vis=1921-293.33000,uranus.33000 device=/xs "select=source(uranus)"<br>
	      mfboot vis=1921-293.35000,uranus.35000 device=/xs "select=source(uranus)"
	    </code>
	    From this point, we measure the best fit flux density model with
	    uvfmeas as before, and redo the entire calibration routine again while
	    specifying the measured fit in the mfcal stage.
	  </div>
	  <div>
	    At this point we consider that the bandpass and flux calibrators have
	    the correct bandpass solution, and are on the correct absolute flux
	    scale. We can now proceed to calibrate the rest of the sources.
	  </div>
	</div> <!-- Bandpass and flux calibration -->
	<div>
	  <a name="measurement-process-source-calibration">&nbsp;</a>
	  <h3>Source calibration</h3>
	  <div>
	    The other sources observed during an epoch can easily be calibrated
	    simply by copying the solutions from the bandpass calibrator, running
	    gpcal, doing some automatic flagging and repeating the process. This,
	    for the most part, is independent of the band that we are calibrating.
	    To keep them on the same flux scale, we run gpboot with the bandpass
	    calibrator as the reference after the gpcal stage. As an example, for
	    a source in the 4cm band, the calibration method might look like the
	    following:
	    <code>
	      gpcopy vis=1934-638.5500 out=0420-014.5500<br>
	      gpcopy vis=1934-638.9000 out=0420-014.9000<br>
	      gpcal vis=0420-014.5500 interval=0.l options=xyvary,qusolve,nopol nfbin=2<br>
	      gpcal vis=0420-014.9000 interval=0.l options=xyvary,qusolve,nopol nfbin=2<br>
	      pgflag vis=0420-014.5500 stokes=xx,yy "command=&lt;b"<br>
	      pgflag vis=0420-014.5500 stokes=yy,xx "command=&lt;b"<br>
	      gpcopy vis=1934-638.5500 out=0420-014.5500<br>
	      gpcopy vis=1934-638.9000 out=0420-014.9000<br>
	      gpcal vis=0420-014.5500 interval=0.l options=xyvary,qusolve,nopol nfbin=2<br>
	      gpcal vis=0420-014.9000 interval=0.l options=xyvary,qusolve,nopol nfbin=2<br>
	      gpboot vis=0420-014.5500 cal=1934-638.5500<br>
	      gpboot vis=0420-014.9000 cal=1934-638.9000<br>
	    </code>
	    We keep using nfbin=2 so that gpboot can also correct for any slightly
	    frequency-dependent effects that may be present in the data.
	  </div>
	  <div>
	    This calibration method is quite robust, and rarely needs manual
	    intervention, due to the way we do the measurement of flux densities.
	    But there is a weakness that will need to be solved at some future
	    point: polarisation calibration is not guaranteed to be very good here.
	    The problem is that during C007 observations, a source might be observed
	    only for a few minutes in one hit, and this includes both the bandpass
	    and flux calibrators as well. Since this is not sufficient parallactic
	    angle coverage from which to reliably determine leakages, the polarisation
	    is not well determined. At low frequencies, where 1934-638 is known to
	    have very small linear polarisations, leakages determined from it are
	    generally not too bad, and polarisation calibration of the other sources
	    is also reasonable so long as we specify options=qusolve,nopol during the
	    gpcal stage (this means that we accept the leakages determined from
	    1934-638). At higher frequencies, there is no real expectation that
	    polarisations will be calibrated correctly.
	  </div>
	  <div>
	    The calibrator database does not currently measure polarisations for
	    each source because of this known weakness, but work is underway to
	    determine some polarisation calibrators at all frequencies so this can
	    be resolved in the future.
	  </div>
	</div> <!-- Source calibration -->
	<div>
	  <a name="measurement-process-flux-model">&nbsp;</a>
	  <h3>Measuring the flux density models</h3>
	  <div>
	    After the calibration process has been completed, we use uvfmeas to
	    determine best fit flux density models. For example, in the 4cm band,
	    here is the procedure for measuring the flux density model for the source
	    2244-372 in the 2012-Apr-22 C007 epoch:
	    <code>
	      uvfmeas vis=2244-372.5500,2244-372.9000 options=plotvec,log order=1 \<br>
	      device=/xs stokes=i
	    </code>
	    The output from this command is:
	    <code><pre>
Source: 2244-372
Stokes I
Vector Average Amplitude:   9.237E-01         Phase:  -1.426E-06
             Uncertainty:   7.311E-01
Scalar Average Amplitude:   9.379E-01   Uncertainty:   7.211E-01
Vector Average Fit Coefficients:
 log S =   1.705E-01
       +  -2.432E-01 x (log f)^ 1
Scatter around fit:   1.384E-02</pre></code>
	    And the plot that is generated is:
	    <img class="needs-border" src="2244-372.uvfmeas.order1.png">
	  </div>
	  <div>
	    It can be seen that the RFI that is still present after flagging
	    in the higher-frequency band is largely ignored by the model
	    fitting process. However, it might be argued that the slope of
	    the model is not following the curve seen in the spectrum
	    properly, and a higher-order fit is required. Using uvfmeas with
	    order=2 results in the output:
	    <code><pre>
Source: 2244-372
Stokes I
Vector Average Amplitude:   9.237E-01         Phase:  -1.426E-06
             Uncertainty:   7.311E-01
Scalar Average Amplitude:   9.379E-01   Uncertainty:   7.211E-01
Vector Average Fit Coefficients:
 log S =   9.104E-02
       +  -4.980E-02 x (log f)^ 1
       +  -1.155E-01 x (log f)^ 2
Scatter around fit:   1.346E-02
	    </pre></code>
	    And a plot that looks like:
	    <img class="needs-border" src="2244-372.uvfmeas.order2.png">
	  </div>
	  <div>
	    The higher-order fit has a slightly smaller scatter around it
	    (13.46 mJy) than does the lower-order fit (13.84 mJy). In the 
	    16cm and 4cm bands, we make both order=1 and order=2 fits and choose 
	    the model that has the lowest scatter to go into the database. So, in 
	    this case, the best fit is:
	    <div class="equation">
	      $\log({\rm S} / 1 {\rm\,Jy}) = 0.09104 - 0.0498\log(\nu / 1 {\rm\,GHz}) - 0.1155\log(\nu / 1{\rm\,GHz})^2.$
	    </div>
	    The "Scatter around fit" value is entered into the database and
	    gets used to estimate the uncertainty of any flux density derived
	    from the model at a particular frequency. With regards to absolute
	    flux density accuracy, simulations of randomly generated calibrators
	    with various spectral indices shows that this measurement method
	    reliably obtains better than 3% accuracy across the entire band
	    regardless of which pair of frequencies is chosen, and so long as
	    the calibrator has a signal-to-noise ratio of 50 or greater, which
	    is not difficult to do over 4 GHz of bandwidth in a couple of minutes.
	  </div>
	  <div>
	    The "Vector Average Amplitude" and "Scalar Average Amplitude" are
	    both entered into the database, and these values allow us to
	    estimate the <a href="#interpreting-defects">defect</a>.
	  </div>
	  <div>
	    The uvfmeas task can also be used to determine the amplitude
	    as a function of $uv$-distance, something that can be useful
	    in determining if a source has structure, or if there is a
	    confusing source in the field. However, if the source has a
	    significant spectral index, then the flux density across the
	    continuum band will change, and since different frequencies will
	    lie at different $uv$-distances, this normal flux variation may
	    be mistaken for structure or confusion.
	  </div>
	  <div>
	    A better idea is to plot the residual amplitude as a function of
	    $uv$-distance. The residual amplitude is simply the flux density
	    at a particular frequency minus the flux density model. For a
	    non-confused point source with a good model, the residual
	    amplitude should be zero (plus or minus the noise level) at all
	    $uv$-distances. Using uvfmeas with the option uvhist makes the
	    following plot:
	    <img class="needs-border" src="2244-372.uvfmeas.order2.uvhist.png">
	  </div>
	  <div>
	    The bottom panel of the plot shows a point for each of the
	    individual frequency channels at each time during the observation
	    of the calibrator, after having the model flux density subtracted.
	    Clearly, putting all those points into the database is not a viable
	    option. Instead, uvfmeas determines the smallest and largest
	    observed $uv$-distances, and makes 100 $uv$-distance bins to fit
	    in this range. An average residual amplitude is calculated in each
	    of these bins, and it is this histogram that is stored in the
	    database. The red line on the bottom panel is the visual representation
	    of this histogram, and for this calibrator you can see that it is
	    very close to zero-valued at all $uv$-distances.
	  </div>
	</div> <!-- Measuring the flux density models -->
	<div>
	  <a name="measurement-process-closure">&nbsp;</a>
	  <h3>Measuring closure phase</h3>
	  <div>
	    The closure phase is measured for each calibrator using the Miriad
	    task closure. Unlike for the flux density models, the closure phase
	    is measured for each IF separately. For example, for an observation
	    made in the 4cm band, we would run closure twice:
	    <code>
	      closure vis=1921-293.5500 stokes=i options=log device=/xs<br>
	      closure vis=1921-293.9000 stokes=i options=log device=/xs
	    </code>
	    From the printed output of this task we take two values and keep them
	    in the database, the measured and theoretical RMS for the closure phase,
	    but this is unfortunately not an indicator of the closure phase
	    itself. To get that, we need to actually read the log file that
	    closure generates, that looks like:
	    <code><pre>
Antennas 1-2-3
  32075.69531250      0.00747906
  32084.92773438      0.03184347
  32094.92773438      0.00064499
  32104.92773438      0.00748781
  32114.92773438      0.02183627
  32124.92773438      0.05054176
Antennas 1-2-4
  32075.69531250      0.01375755
  32084.92773438     -0.00359855
  32094.92773438     -0.00518243
  32104.92773438     -0.00782766
  32114.92773438     -0.00175100
  32124.92773438      0.01889207
	    ....</pre></code>
	  </div>
	  <div>
	    For each three-antenna set, the log has a time value in the
	    first column (specified as the number of seconds after the start
	    of the observation epoch) and the closure phase value in degrees in
	    the second column. To obtain a single value for the closure phase
	    we simply take each closure phase value on all baselines and take
	    the average. This average closure phase is stored in the database.
	  </div>
	</div> <!-- Measuring closure phase -->
	<div>
	  <a name="measurement-process-miscellaneous">&nbsp;</a>
	  <h3>Measuring miscellaneous parameters</h3>
	  <div>
	    There are several miscellaneous bits of information that the
	    database stores that are useful to have, but can be a little tricky
	    to obtain.
	  </div>
	  <div>
	    The source name, right ascension and declination of the observation,
	    the time of the first and last cycles on source, the actual
	    amount of integration time and the exact frequency configuration
	    are all gathered from the uvindex task.
	    This task is very easy to run:
	    <code>
	      uvindex vis=1921-293.5500
	    </code>
	    It produces output similar to the following:
	    <code><pre>
Summary listing for data-set 1921-293.5500/

       Time        Source        Antennas Spectral Wideband  Freq  Record
                    Name        Calcode   Channels Channels Config   No.

12APR22:21:56:35.7 1921-293         n  6      2049        0      1       1
12APR22:21:57:24.9 Total number of records                             360

------------------------------------------------

Total observing time is  0.02 hours

The input data-set contains the following frequency configurations:

Frequency Configuration 1
  Channels  Freq(chan=1)  Increment  Restfreq     IFChain
    2049       4.47600    0.0010000   0.00000 GHz     1

------------------------------------------------

The input data-set contains the following polarizations:
There were 90 records of polarization YX
There were 90 records of polarization XY
There were 90 records of polarization YY
There were 90 records of polarization XX

------------------------------------------------

The input data-set contains the following pointings:
 Source       CalCode     RA            DEC             dra(arcsec) ddec(arcsec)
1921-293         n     19:24:51.06   -29:14:30.12           0.00         0.00

------------------------------------------------</pre></code>
	  </div>
	  <div>
	    The script that adds data to the database interprets the
	    first and last times listed in the top section, and stores them
	    in the database as <a href="https://en.wikipedia.org/wiki/Julian_day">
	      MJDs</a>. The total amount of integration time (accounting for
	    flagging) is calculated by uvindex and is output as the "Total
	    observing time" in hours.
	  </div>
	  <div>
	    The frequency configuration of the set is given as the number of
	    channels, the frequency of the first channel and the frequency spacing
	    between channels. From this we can tell which correlator mode was
	    being used, and the sideband. Although this information is not
	    readily available from the calibrator database web interface, it is
	    stored and may be made available should it be required.
	  </div>
	  <div>
	    The source name, and the position it was observed at are shown in
	    the bottom section of the uvindex output. The R.A. and Dec of each
	    observation is stored separately to the nominal position of the
	    calibrator, so we can tell if there is a discrepancy between the
	    observed and "proper" coordinates.
	  </div>
	  <div>
	    To determine the array that was used for the observations we use
	    the uvlist task:
	    <code>
	      uvlist vis=1921-293.5500 options=array,full
	    </code>
	    The output of this task looks like:
	    <code><pre>
UV Listing for data-set 1921-293.5500/

Options: full,array

------------------------------------------------------------
Telescope: ATCA
Latitude:   -30:18:46.38
Longitude: +149:33:00.50
Mounts: Alt-az

Antenna positions in local equatorial coordinates

        X (meters)     Y (meters)     Z (meters)
        ----------     ----------     ----------
  1         0.0000         0.0000         0.0000
  2        -0.0209       -30.6222         0.0090
  3        -0.1162      -107.1460         0.0020
  4        -0.1710      -153.0710        -0.0010
  5        -0.3952      -352.0463         0.0140
  6        -5.1442     -4438.7747         0.0600</pre></code>
	  </div>
	  <div>
	    Antenna 1 is always listed at the origin in this output, but it
	    is actually antenna 6 that never moves, so we begin by adding
	    the required length to each position to make antenna 6 appear
	    at (0, 0, 0). The X direction represents North-South (positive
	    is North), and the Y direction represents
	    East-West (positive is East). Since CA06 is always on station
	    W392, and stations are numbered based on the station interval
	    being 15.3m, it is straightforward to take these numbers and
	    calculate which stations each antenna is on. In this case,
	    CA01 is on W102, CA02 is on W104, CA03 is on W109,
	    CA04 is on W112, CA05 is on W125 and CA06 is, as always, on W392.
	  </div>
	  <div>
	    A <a href="http://www.narrabri.atnf.csiro.au/observing/users_guide/html/new_atug_57.html#Array-Configurations">
	      table of configurations</a> is available, and with it we can match the
	    array that was used. These stations correspond to the EW352
	    array.
	  </div>
	</div> <!-- Measuring miscellaneous parameters -->
      </div>

      <div class="documentation-section">
	<a name="web-interface">&nbsp;</a>
	<h2>Using the web interface</h2>
	<div>
	  <a name="front-page-recent-changes">&nbsp;</a>
	  <h3>Front Page: Recent Database Changes</h3>
	  <img src="front-page-recent-changes.png">
	  <div>
	    Each time the database is changed, a record is kept that summarises the
	    change. Most of the time, this change will be a new epoch of measurements
	    by the C007 or C1730 projects becoming available, but changes to
	    calibrator position or recomputation of flux densities will also be
	    tracked.
	  </div>
	  <div>
	    This section of the front page will always show the three most recent
	    changes to the database. To get a full list of changes, and a list of all
	    the measurement epochs in the database, click the "show all changes and
	    epochs" link at the bottom right of the section.
	  </div>
	  <div>
	    For new measurement epochs, a "show epoch" link will be shown in the
	    summary box; clicking this link will take you to a page that summarises
	    the sources, bands and flux densities observed during that epoch.
	  </div>
	</div> <!-- Front Page: Recent Database Changes -->
	<div>
	  <a name="front-page-quick-find-calibrator">&nbsp;</a>
	  <h3>Front Page: Quick-find Calibrator</h3>
	  <img src="front-page-quick-find-calibrator-1.png">
	  <div>
	    If you know the name of the calibrator you are interested in, and
	    just want to get a quick summary of the latest flux density measurements
	    in each band for that calibrator, you can very quickly get this
	    information.
	  </div>
	  <div>
	    On the left of this section, you will see an input box asking for a
	    calibrator name. As you enter the name of the calibrator, the input box
	    will display the sources known to the database that match the entry
	    you have made so far. You can select the source from the dropdown box or
	    continue to type in the name yourself.
	  </div>
	  <div>
	    Once you have selected or typed the name of a calibrator in the left
	    box, and pressed Enter or otherwise removed the focus from the input box,
	    the interface will query the database. Once the results have come back
	    from the server (which should occur in just a few seconds), the right
	    side of the section should display the position of the calibrator, the
	    rise and set LST at the ATCA, and the flux densities at some of the
	    ATCA recommended continuum frequencies. If no observation of the source
	    can be found in a particular band, the flux density for that band's
	    recommended frequency will read "N/A" (not available).
	  </div>
	  <img src="front-page-quick-find-calibrator-2.png">
	  <div>
	    The "more information..." link at the bottom of the table of flux
	    densities can be used to bring up a page that more contains much
	    more information about the source.
	  </div>
	</div> <!-- Front Page: Quick-find Calibrator -->
	<div>
	  <a name="front-page-search-for-calibrators">&nbsp;</a>
	  <h3>Front Page: Search for Calibrators</h3>
	  <img src="front-page-search-for-calibrators.png">
	  <div>
	    The instructions on the left of this section give a reasonable guide on
	    how to search for a useful calibrator. This help section will thus be very brief,
	    and will give only some more detail on the use of the "Position" box.
	  </div>
	  <div>
	    While entering a right ascension and declination
	    (e.g. "19:39:25.026 -63:42:45.63") is a perfectly good way to use the
	    "Position" box, most people are likely to be actually searching for
	    calibrators around a known source rather than some arbitrary position.
	    To make such a search easier, the "Position" box will detect if an
	    entry looks unlike an R.A. / Dec. pair and then assume it is the name
	    of an astronomical source which can be located with the help of the
	    <a href="http://cds.u-strasbg.fr/cgi-bin/Sesame">Sesame name resolver</a>.
	  </div>
	  <div>
	    If you enter a source name then (e.g. "NGC 612"), and press Enter or
	    otherwise take focus away from the "Position" box, you will get an
	    animated box to let you know that the name is being resolved. Once the
	    resolution has completed successfully, the box will be filled with the
	    appropriate R.A. / Dec. (in this case "01:33:58 -36:29:36") and the
	    animated box will turn solid green, and will show the name of the source
	    that was just resolved. If the name resolution failed, the box will turn
	    red, and will indicate the failure.
	  </div>
	  <div>
	    The "Search" button can now be used to search for calibrators around the
	    position.
	  </div>
	</div> <!-- Front Page: Search for Calibrators -->
	<div>
	  <a name="change-page-database-change-summary">&nbsp;</a>
	  <h3>Change Page: Database Change Summary</h3>
	  <img src="change-page-database-change-summary.png">
	  <div>
	    The change summary gives a full list of all the changes made to the
	    database since its creation. Each change is given a small description,
	    which is shown in this table. The time that each change was made is shown
	    on the left of the table, and this time is in the local time zone (Sydney)
	    will reflect daylight savings time if appropriate.
	  </div>
	  <div>
	    If the change relates to flux density measurements, then clicking on the
	    description text will bring up a page that will show all the sources
	    observed during the related epoch, and the flux densities measured in
	    each band during that epoch.
	  </div>
	  <div>
	    If the change relates to a change in the details of a particular calibrator,
	    then clicking on the description text will bring up a page that describes
	    that calibrator, and the measurements in the database for that calibrator.
	  </div>
	</div> <!-- Change Page: Database Change Summary -->
	<div>
	  <a name="change-page-epochs">&nbsp;</a>
	  <h3>Change Page: Epochs</h3>
	  <img src="change-page-epochs.png">
	  <div>
	    Since the majority of measurements in the ATCA calibrator database are
	    obtained from the C007 and C1730 projects, this section is here to allow
	    the user to easily see the epochs of these projects that have contributed
	    data to the database.
	  </div>
	  <div>
	    The table itself will appear almost immediately after the page is loaded,
	    and will be populated with a row for each of the epochs the database
	    uses, with earlier epochs listed first. For each epoch, the project code
	    it used, along with the full time range of observations and the array
	    configuration at the time are given.
	  </div>
	  <div>
	    After the page has loaded, the table will begin to query the database
	    for a more complete summary of each epoch (since this will take some
	    time to compile). Sometime later, each row will also list the number
	    of unique sources that were observed during that epoch, and the
	    frequency bands that measurements were made in. Clicking the number in
	    the "# Sources" column will bring up a page that will show all the sources
	    observed during that epoch, and the flux densities measured in each band
	    for those sources.
	  </div>
	</div> <!-- Change Page: Epochs -->
	<div>
	  <a name="epoch-page">&nbsp;</a>
	  <h3>Epoch Page: Epoch Summary and Epoch Observations</h3>
	  <img src="epoch-page-epoch-summary.png">
	  <div>
	    The epoch summary gives a very similar set of information to that
	    found on the "Epochs" section on the change page: the project code,
	    the array used during the observations and the epoch time range are
	    all shown as soon as the page as loaded.
	  </div>
	  <div>
	    The page also queries the database for each source that was observed
	    during the epoch, and then determines:
	    <ul>
	      <li>the bands that were observed in,</li>
	      <li>the number of unique sources that were observed in each band,
		and during the epoch as a whole (shown in the "# Sources" row
		in the table in the "Epoch Summary" section), and</li>
	      <li>the amount of integration time obtained over all the sources
		in each band (shown in the "Integration Time" row in the
		table in the "Epoch Summary" section).</li>
	    </ul>
	  </div>
	  <div>
	    After the sources that were observed in the epoch are found in the
	    database, the table in the "Epoch Observations" section is shown.
	  </div>
	  <img src="epoch-page-epoch-observations.png">
	  <div>
	    Lower frequency observations are shown to the left in this table.
	    For each unique source that was observed, two columns are shown per band:
	    <ul>
	      <li>In the column labelled "Since Start (Int. Time)" are shown two
		values, the first being the time since the start of the epoch that
		the source was observed at in that band (in minutes), and the second
		(in parentheses) being the amount of integration time obtained for
		that source in that band (again, in minutes).</li>
	      <li>The flux density measured from this data, and its associated
		uncertainty in Jy, evaluated at the lowest recommended frequency
		in that band.</li>
	    </ul>
	  </div>
	  <div>
	    The sources are ordered in the table such that the sources observed first are listed
	    first. Each source name is a link to a page that thoroughly describes
	    the information that the calibrator database has about that source.
	  </div>
	</div> <!-- Epoch Page: Epoch Summary and Epoch Observations -->
	<div>
	  <a name="search-page-search-results">&nbsp;</a>
	  <h3>Search Page: Search Results</h3>
	  <div>
	    If you used the <a href="#front-page-search-for-calibrators">search section
	      on the front page</a> to find calibrators within some distance of some
	    specified coordinate, the "Search Results" section might look something like
	    the image below.
	  </div>
	  <img src="search-page-search-results-1.png">
	  <div>
	    In the area above the "Search Results" section is a human-readable summary
	    of how the interface interpreted the search parameters. After some time
	    querying the database (during which time the message
	    "Searching the database, please wait..." will be shown in place of the
	    table shown in the image above), the table will appear with the search
	    results.
	  </div>
	  <div>
	    The calibrators found that match the search query will be ordered by the distance
	    to the specified coordinates, with closer calibrators listed first. The distance
	    between the specified coordinates and each calibrator is given in the column
	    labelled "Distance" in degrees. The R.A. and Dec. of each calibrator is given in
	    the appropriately named columns, and each coordinate is rounded to the
	    nearest arcsec for brevity. To look at more detailed information about a
	    particular calibrator, click its name in the left-most column.
	  </div>
	  <div>
	    For each calibrator, the latest flux density in each band is found in the database,
	    and listed in the appropriate column on the right of the table.
	    If no flux density measurement has been made in a particular band, that column
	    will remain empty.
	  </div>
	  <div>
	    If you searched for calibrators within a block of R.A. and Dec., the
	    "Search Results" section might look like the image below.
	  </div>
	  <img src="search-page-search-results-2.png">
	  <div>
	    In this case, the "Distance" column is not shown, but in all other regards the
	    tables are the same.
	  </div>
	</div> <!-- Search Page: Search Results -->
	<div>
	  <a name="view-page-source-information">&nbsp;</a>
	  <h3>View Page: Source Information</h3>
	  <img src="view-page-source-information.png">
	  <div>
	    When viewing detailed information about a particular calibrator, the topmost
	    section will be filled with basic information about the source, as shown
	    above. The R.A. and Dec. of the source is shown, with the full accuracy
	    available in the database, along with which catalogue it was taken from,
	    the positional uncertainty, and in some cases, a link to the catalogue.
	  </div>
	  <div>
	    After the information is retrieved from the database, the web page itself
	    calculates the LST when this source rises above the 12&deg; elevation limit
	    at ATCA, and the LST when it sets below the limit. These LSTs are shown in
	    the "ATCA Rise/Set LST" row on the left.
	  </div>
	  <div>
	    For sources that have declinations -88&deg; &lt; &delta; &le; -39&deg;,
	    -27&deg; &lt; &delta; &le; -9&deg; or 0&deg; &lt; &delta; &le; 77&deg;,
	    a link will be made to <a href="http://skyview.gsfc.nasa.gov/">NASA's SkyView</a>
	    service in order to quickly see an image of this source from the PMN/GB6
	    survey. This link will be in the "Images/References" table on the left;
	  </div>
	  <div>
	    For sources that have declinations south of -30&deg;, a link will be
	    made to SkyView in order to quickly see an image of this source from the
	    SUMSS. For sources that have declinations north of -39&deg;, a link
	    will be made to SkyView in order to quickly see an image of this source
	    from the NVSS.
	  </div>
	  <div>
	    A link will also always be made to the <a href="http://ned.ipac.caltech.edu/">
	      NASA/IPAC Extragalactic Database (NED)</a> that will do a "near position"
	    search around the calibrator's coordinates.
	  </div>
	</div> <!-- View Page: Source Information -->
	<div>
	  <a name="view-page-notes">&nbsp;</a>
	  <h3>View Page: Notes</h3>
	  <img src="view-page-notes">
	  <div>
	    The database may have important notes about a calibrator, that may
	    describe, for example, situations in which the calibrator might not
	    be suitable. When the database has such notes, they will be shown in this
	    section.	    
	  </div>
	  <div>
	    If the database does not have any notes for the calibrator being viewed,
	    the text "There are no notes in the database for this source" will be
	    shown in this section instead.
	  </div>
	  <div>
	    In some cases (usually when viewing a source from a C1730 epoch), you will
	    be able to view the measurements made for a source that is not actually
	    in the ATCA calibrator list. In this case, you will see the message
	    "This source is not in the calibrator database". Any information shown
	    about this source in the <a href="#view-page-source-information">"Source
	      Information"</a> section will come from an actual observation at a
	    specified epoch.
	  </div>
	  <div>
	    The warning for 16cm observers, seen at the bottom of the image above, will
	    always be shown in this section.
	  </div>
	  <div>
	    If you are viewing information about a calibrator you know very well, and think
	    that you have information about it that other observers should know,
	    please feel free to send an email to <a href="mailto:calibrators@atnf.csiro.au">
	      the calibrators list</a> with the information; we'd be happy to add it as
	    a note into the calibrator database.
	  </div>
	</div> <!-- View Page: Source Notes -->
	<div>
	  <a name="view-page-flux-density-measurements">&nbsp;</a>
	  <h3>View Page: Flux Density Measurements</h3>
	  <img src="view-page-flux-density-measurements.png">
	  <div>
	    This table summarises the latest measurements made for this calibrator.
	    For each of the ATCA frequency bands, the page will get the latest
	    <a href="#interpreting-flux-densities">flux density model</a> from the 
	    database, and evaluate it at one or more of the recommended frequencies 
	    in that band. The evaluated flux densities are shown in the appropriate
	    row of the table, along with the UTC date that the model was measured at.
	  </div>
	  <div>
	    If no model can be found for a particular band for the calibrator being
	    viewed, the flux density and date will be shown as "N/A" (not available).
	  </div>
	  <div>
	    The page will also get the latest
	    <a href="#interpreting-defects">defect and closure phase</a> information
	    for the calibrator being viewed in each band, and in each different array
	    group. This information is shown in the "Defect / Closure Phase"
	    columns on the right of the table. No date is given for each of these
	    values, but one of the values shown will correspond to the same epoch
	    in which the flux density model was measured.
	  </div>
	</div> <!-- View Page: Flux Density Measurements -->
	<div>
	  <a name="view-page-flux-density-time-series">&nbsp;</a>
	  <h3>View Page: Flux Density Time Series</h3>
	  <img src="view-page-flux-density-time-series.png">
	  <div>
	    This plot shows how the flux density of the calibrator has changed over
	    time in each of the ATCA frequency bands. Because the
	    <a href="#interpreting-flux-densities">flux densities</a> in the
	    calibrator database are actually represented as models fit to the
	    data during the measurement procedure, the flux densities can
	    be evaluated at a consistent frequency regardless of the frequencies
	    actually observed in any epoch (in the same band). This allows us to
	    do a much more accurate comparison between flux densities measured
	    in multiple epochs.
	  </div>
	  <div>
	    In the plot above we see that the flux density of this calibrator
	    (1934-638 in this case) is different in each of the bands (as expected).
	    Since the flux density of the calibrator would be different depending on
	    the frequency, only a single frequency is chosen per band, and these
	    frequencies are shown at the top of the plot next to the "Show" label,
	    in MHz.
	  </div>
	  <div>
	    Since there are many plots on the calibrator view page, a consistent
	    colour scheme is used across them all.
	    <table class="band-plot-colours">
	      <thead>
		<tr><th>Band Name</th><th>Colour</th><th>Symbol</th></tr>
	      </thead>
	      <tbody>
		<tr class="text16cm"><th>16cm</th><td>Vermillion</td>
		  <td>circle</td></tr>
		<tr class="text4cm"><th>4cm</th><td>Fuchsia</td>
		  <td>square</td></tr>
		<tr class="text15mm"><th>15mm</th><td>Gold</td>
		  <td>diamond</td></tr>
		<tr class="text7mm"><th>7mm</th><td>Orange</td>
		  <td>triangle</td></tr>
		<tr class="text3mm"><th>3mm</th><td>Plum</td>
		  <td>inverted triangle</td></tr>
	      </tbody>
	    </table>
	  </div>
	  <div>
	    Each of the buttons in the legend next to the "Show" label is coloured
	    if there is data on the plot in that band. If there is no data available
	    to plot in a particular band, that band's button will be coloured
	    <span class="textdisabled">grey</span>. Clicking a band's button (if it
	    is not coloured <span class="textdisabled">grey</span>) will remove the
	    data from that band from each of the plots on the view page, and the
	    button will then appear slightly transparent (but will still have the
	    same band colour). To add the data from that band back to the plots,
	    click the band button again.
	  </div>
	  <div>
	    When the data shown on this plot changes (as bands are added or removed
	    from it), the y-axis range will change to keep all the data comfortably
	    on the plot. The x-axis range is fixed, regardless of the
	    epochs that are actually available for this calibrator.
	  </div>
	</div> <!-- View Page: Flux Density Time Series -->
	<div>
	  <a name="view-page-spectral-index-time-series">&nbsp;</a>
	  <h3>View Page: Spectral Index Time Series</h3>
	  <img src="view-page-spectral-index-time-series.png">
	  <div>
	    This plot shows how the spectral index of the calibrator has changed
	    over time in each of the ATCA frequency bands. Because the
	    <a href="#interpreting-spectral-indices">spectral indices</a> are
	    computed from the flux density models in the calibrator database at
	    a consistent frequency, the spectral index should stay reasonably
	    constant with time, unless physical changes in the calibrator
	    cause the emission mechanism to vary, or the flux model is inaccurate.
	  </div>
	  <div>
	    In the plot above we see that the spectral index of this calibrator
	    (1934-638 in this case) is different in each of the bands (as expected
	    since 1934-638 is a GPS source).
	    Since the spectral index of the calibrator would be different depending on
	    the frequency, only a single frequency is chosen per band, and these
	    frequencies are shown at the top of the plot next to the "Show" label,
	    in MHz.
	  </div>
	  <div>
	    Since there are many plots on the calibrator view page, a consistent
	    colour scheme is used across them all.
	    <table class="band-plot-colours">
	      <thead>
		<tr><th>Band Name</th><th>Colour</th><th>Symbol</th></tr>
	      </thead>
	      <tbody>
		<tr class="text16cm"><th>16cm</th><td>Vermillion</td>
		  <td>circle</td></tr>
		<tr class="text4cm"><th>4cm</th><td>Fuchsia</td>
		  <td>square</td></tr>
		<tr class="text15mm"><th>15mm</th><td>Gold</td>
		  <td>diamond</td></tr>
		<tr class="text7mm"><th>7mm</th><td>Orange</td>
		  <td>triangle</td></tr>
		<tr class="text3mm"><th>3mm</th><td>Plum</td>
		  <td>inverted triangle</td></tr>
	      </tbody>
	    </table>
	  </div>
	  <div>
	    Each of the buttons in the legend next to the "Show" label is coloured
	    if there is data on the plot in that band. If there is no data available
	    to plot in a particular band, that band's button will be coloured
	    <span class="textdisabled">grey</span>. Clicking a band's button (if it
	    is not coloured <span class="textdisabled">grey</span>) will remove the
	    data from that band from each of the plots on the view page, and the
	    button will then appear slightly transparent (but will still have the
	    same band colour). To add the data from that band back to the plots,
	    click the band button again.
	  </div>
	  <div>
	    When the data shown on this plot changes (as bands are added or removed
	    from it), niether the x-axis or y-axis range will change, as they are both
	    fixed.
	  </div>
	</div> <!-- View Page: Spectral Index Time Series -->
	<div>
	  <a name="view-page-flux-model">&nbsp;</a>
	  <h3>View Page: Flux Model</h3>
	  <img src="view-page-flux-model.png">
	  <div>
	    This plot attempts to illustrate the latest flux density models that have
	    been measured for this calibrator. It does this by evaluating the
	    <a href="#interpreting-flux-densities">flux density models</a> measured
	    in each band (in the most recent epoch they were obtained) at several
	    frequencies across the band, and a line is drawn between these points.
	  </div>
	  <div>
	    In the plot above we see that the flux density models of this calibrator
	    (1934-638 in this case) are different in each of the bands (as expected),
	    but they seem to join quite smoothly together. This is what is expected
	    for a calibrator that has a constant flux density with time. If however the
	    calibrator is varying, the flux models may appear quite disjoint from one
	    another, unless the models in each band were made from epochs closely
	    spaced in time.
	  </div>
	  <div>
	    Since there are many plots on the calibrator view page, a consistent
	    colour scheme is used across them all. The following table shows the colours
	    that represent each band, and also the frequency range that the models
	    are evaluated over.
	    <table class="band-plot-colours">
	      <thead>
		<tr><th>Band Name</th><th>Colour</th><th>Symbol</th>
		  <th>Freq. Range (MHz)</th></tr>
	      </thead>
	      <tbody>
		<tr class="text16cm"><th>16cm</th><td>Vermillion</td>
		  <td>circle</td><td>700 - 3300</td></tr>
		<tr class="text4cm"><th>4cm</th><td>Fuchsia</td>
		  <td>square</td><td>4000 - 12000</td></tr>
		<tr class="text15mm"><th>15mm</th><td>Gold</td>
		  <td>diamond</td><td>16000 - 25000</td></tr>
		<tr class="text7mm"><th>7mm</th><td>Orange</td>
		  <td>triangle</td><td>30000 - 50000</td></tr>
		<tr class="text3mm"><th>3mm</th><td>Plum</td>
		  <td>inverted triangle</td><td>85000 - 105000</td></tr>
	      </tbody>
	    </table>
	  </div>
	  <div>
	    Each of the buttons in the legend next to the "Show" label is coloured
	    if there is data on the plot in that band. If there is no data available
	    to plot in a particular band, that band's button will be coloured
	    <span class="textdisabled">grey</span>. Clicking a band's button (if it
	    is not coloured <span class="textdisabled">grey</span>) will remove the
	    data from that band from each of the plots on the view page, and the
	    button will then appear slightly transparent (but will still have the
	    same band colour). To add the data from that band back to the plots,
	    click the band button again.
	  </div>
	  <div>
	    When the data shown on this plot changes (as bands are added or removed
	    from it), the y-axis range will change to keep all the data comfortably
	    on the plot. The x-axis range is fixed to contain the entire range of
	    frequencies shown in the table above, regardless of frequency bands
	    that are actually available for this calibrator. The x-axis is also shown
	    logarithmically.
	  </div>
	  
	</div> <!-- View Page: Flux Model -->
	<div>
	  <a name="view-page-structure-plot">&nbsp;</a>
	  <h3>View Page: Structure Plot</h3>
	  <img src="view-page-structure-plot.png">
	  <div>
	    This plot shows the histogram points measured by the uvfmeas task in
	    each epoch, as described in the
	    <a href="#measurement-process-flux-model">section regarding the
	      measurement of flux models</a> above. For each band, the five most
	    recent histograms are obtained from the database and shown here.
	  </div>
	  <div>
	    For a good calibrator, we expect that the residual amplitude should be
	    zero at all $uv$-distances. The plot above does not show this to be
	    the case for 1934-638, which we know is a good calibrator. Looking at
	    the colours of the points that deviate from zero shows that short baselines
	    at low frequencies are the biggest outliers. This can be attributed to
	    low-level RFI in the most part, as the deviations do not exceed 0.2 Jy for
	    a source that is much stronger than 3 Jy over most of the frequency range
	    that we see deviations for.
	  </div>
	  <div>
	    Our general recommendation for interpreting this plot is to look for
	    significant deviations (usually much larger than 1% of the source
	    flux density) and to be concerned only if the deviations seem to have
	    a recognisable pattern to them. In the plot above, the deviations are
	    semi-random with plenty of discontinuities.
	  </div>
	</div> <!-- View Page: Structure Plot -->
      </div>

      <div class="documentation-section">
	<a name="interpreting-the-measurements">&nbsp;</a>
	<h2>Interpreting the measurements</h2>
	<div>
	  <a name="interpreting-flux-densities">&nbsp;</a>
	  <h3>Flux Densities</h3>
	  <div>
	    Flux densities are shown by the calibrator database either at a particular
	    frequency (such as on the calibrator-specific page) or in a particular band
	    (such as on the epoch view pages). The flux densities are obtained by
	    evaluating the model that was fit to the visibilities during the data
	    reduction at a specific frequency. On some pages this frequency is
	    explicitly specified, but when only the band is specified, the
	    frequencies are set to be the lowest recommended frequency in that band, as
	    shown in the following table.
	  </div>
	  <table id="band-recommended-frequencies">
	    <thead>
	      <tr><th>Band Name</th><th>Evaluation Frequency (MHz)</th></tr>
	    </thead>
	    <tbody>
	      <tr><th>16cm</th><td>2100</td></tr>
	      <tr><th>4cm</th><td>5500</td></tr>
	      <tr><th>15mm</th><td>17000</td></tr>
	      <tr><th>7mm</th><td>33000</td></tr>
	      <tr><th>3mm</th><td>93000</td></tr>
	    </tbody>
	  </table>
	  <div>
	    For example, the model measured for 1934-638 during the 2010-JUL-03 epoch
	    (in the 16cm band) is:
	    <div class="equation">
	      $\log {\rm S}(\nu) = 1.180 + 0.1769\times\log \nu - 1.355\times(\log \nu)^2,$
	    </div>
	    where $\rm{S}$ is the flux density in Jy, and $\nu$ is the frequency in GHz. Thus,
	    if the 16cm flux density is specified on one of the calibrator database pages, it
	    is derived from:
	    <div class="equation">
	      \[\begin{eqnarray}
	      {\rm S}(2.1) & = & 10^{1.180 + 0.1769\times\log(2.1) - 1.355\times(\log(2.1))^2} \\
	      & = & 12.483 {\,\rm Jy}
	      \end{eqnarray} \]
	    </div>
	  </div>
	  <div>
	    Each flux density is usually accompanied by an uncertainty after a $\pm$ symbol.
	    For example, the flux density above would usually be given as $12.483\pm0.002$ Jy.
	    This uncertainty comes from the RMS value of the visibility amplitudes after the
	    measured fit is subtracted.
	  </div>
	  <div>
	    On all pages where the flux density is shown as a number, both it and the
	    associated uncertainty are rounded to the nearest mJy.
	  </div>
	  <div>
	    In general, observations made by the C007 calibrator project will reach
	    sensitivities of around a few mJy. If the scatter around the fit is observed to
	    be more than 10 mJy, the associated flux density should be treated with some
	    suspicion. If the scatter is more than 100 mJy then the flux density is probably
	    incorrect, as there will likely have been some problem with the data.
	  </div>
	</div>
	<div>
	  <a name="interpreting-defects">&nbsp;</a>
	  <h3>Defects and Closure Phases</h3>
	  <div>
	    The defects and closure phases displayed in the "Flux Density Measurements"
	    section on the calibrator page give an indication of the suitability of the
	    source for calibration purposes.
	  </div>
	  <div>
	    During the flux density measurement process, both the scalar-averaged and
	    vector-averaged flux density is measured for each band as a whole. We assume
	    that the vector-averaged flux density represents primarily the flux present
	    within the resolution element at the phase centre of the observation, which
	    is set to be the known position of the calibrator. The scalar-averaged
	    flux density should represent the amplitude response of the primary beam,
	    which is not restricted to the source at the phase centre, and should always
	    be equal to or larger than the vector-averaged flux density.
	  </div>
	  <div>
	    The defect is defined to be:
	    <div class="equation">
	      ${\rm defect} = ( [{\rm S}_{sca} / {\rm S}_{vec}] - 1)\times 100\%,$
	    </div>
	    where ${\rm S}_{sca}$ is the scalar-averaged flux density, and
	    ${\rm S}_{vec}$ is the vector-averaged flux density.
	  </div>
	  <div>
	    But the defect itself is not a good summary of a calibrator's quality, as
	    there could be a number of reasons for a non-zero defect (which we'll
	    describe later). For this reason, we measure another quantity during the reduction
	    process: <a href="#measurement-process-closure">the closure phase</a>. 
	    If there is a point-like component in
	    the field then the average closure phase measured by each set of three antenna
	    should be zero for that component, regardless of the position of the
	    component within the field. If the component is not point-like, then
	    the closure phase will be non-zero.
	  </div>
	  <div>
	    Of course there may be more than one component in the field, but
	    brighter components will influence the measured closure phase more than
	    fainter components.
	  </div>
	  <div>
	    Taken together, the defect and closure phase gives us an idea of what
	    the calibrator field may be like, as summarised in the following table.
	  </div>
	  <table id="defect-closurephase-meanings">
	    <tr><th>Defect</th><th>Closure Phase</th><th>Interpretation</th></tr>
	    <tr><td><span class="qualityGood">small</span></td>
	      <td><span class="qualityGood">small</span></td><td>A dominant point source at the phase
		centre; little to no confusion.</td></tr>
	    <tr><td><span class="qualityWarn">moderate</span></td>
	      <td><span class="qualityGood">small</span></td><td>Probable confusing source within
		the field, bright enough to cause issues with calibration.</td></tr>
	    <tr><td><span class="qualityBad">large</span></td>
	      <td><span class="qualityGood">small</span></td><td>Either a confusing source with a very
		similar brightness to the source at the phase centre, or likely to be
		a point source offset from the phase centre (i.e. a calibrator observed
		at the wrong position).</td></tr>
	    <tr><td><span class="qualityWarn">moderate</span> - 
		<span class="qualityBad">high</span></td>
	      <td><span class="qualityWarn">moderate</span> - 
		<span class="qualityBad">high</span></td>
	      <td>Significantly resolved structure bright enough to make
		calibration very difficult.</td></tr>
	  </table>
	  <div>
	    To assist with the use of these classifications, the defects and
	    closure phases are colour-coded where they are displayed. "Small"
	    defects and closure phases are coloured <span class="qualityGood">green</span>,
	    "moderate" values are coloured <span class="qualityWarn">orange</span>,
	    and "high" values are coloured <span class="qualityBad">red</span>.
	  </div>
	  <div>
	    Since a "point-like component" is simply a source of flux density
	    that is unresolved by the interferometer, it is clear that the
	    definition is dependent on the interferometer's resolving power. This
	    is why the defects and closure phases are reported for various array
	    sizes. These values come only from arrays with maximum baselines
	    less than or equal to the length given in the header above the column.
	    For example, values given in the column headed by "1.5km" come only from
	    1.5 arrays (1.5A, B, C or D). You should use the numbers corresponding
	    to the array you plan on using in assessing the suitability of a
	    particular calibrator.
	  </div>
	</div>
	<div>
	  <a name="interpreting-spectral-indices">&nbsp;</a>
	  <h3>Spectral Indices</h3>
	  <div>
	    Spectral indices are shown by the calibrator database at a particular
	    frequency, which is usually listed near to the spectral index value
	    itself. The spectral indices are obtained by evaluating the derivative
	    of the model that was fit to the visibilities during the data reduction
	    at this particular frequency.
	  </div>
	  <div>
	    We define the spectral index of a source by noting that for most
	    sources the observed flux density is dependent on the observing
	    frequency via
	    <div class="equation">
	      ${\rm S} \propto \nu^{\alpha},$
	    </div>
	    where ${\rm S}$ is the flux density at some frequency $\nu$, and
	    $\alpha$ is the spectral index. We define $\alpha$ such that
	    negative values indicate that the flux density decreases with
	    increasing frequency.
	  </div>
	  <div>
	    Measuring a source's spectral index is thus generally achieved by
	    measuring $\log {\rm S}$ at multiple $\log \nu$ and fitting a line, of
	    which $\alpha$ is the slope. But this is not always possible. The
	    calibrator database stores models with up to 3 coefficients in each
	    of the models:
	    <div class="equation">
	      \[\begin{eqnarray}
	      \log {\rm S} & = & a + b\times \log \nu + c\times(\log \nu)^2 \\
	      {\rm S} & = & a + b\times\nu + c\times\nu^2
	      \end{eqnarray} \]
	    </div>
	    The logarithmic models are used for the vast majority of the calibrators
	    in the database, but for those calibrators with flux densities near zero
	    (and thus with flux densities in a particular channel that may be
	    negative), the non-logarithmic models are used.
	  </div>
	  <div>
	    The spectral index is just the rate of change of $\log {\rm S}$ with
	    $\log \nu$, which is easy to compute for the logarithmic model:
	    <div class="equation">
	      $\alpha \equiv d\log{\rm S}/d\log\nu = b + 2c\times\log\nu.$
	    </div>
	    It is straightforward to see that if $c = 0$, then $\alpha = b$ as
	    expected.
	  </div>
	  <div>
	    For the non-logarithmic model, we first have to do some substitution:
	    <div class="equation">
	      $\log {\rm S} = \log (a + b\times\nu + c\times\nu^2).$
	    </div>
	    If we call $x \equiv \log\nu$, then $\nu = 10^x$, and the equation
	    above becomes:
	    <div class="equation">
	      $\log {\rm S} = \log (a + b\times10^x + c\times10^{2x}).$
	    </div>
	    We can take the derivative of this now (thanks to
	    <a href="http://www.wolframalpha.com/">Wolfram Alpha</a>):
	    <div class="equation">
	      $\alpha \equiv d\log {\rm S}/dx = 10^x(b + 2^{x+1}\times5^xc)/(a+10^x(b+c10^x)).$
	    </div>
	    This can be further simplified by reversing the previous substitution
	    and identifying the denominator as simply the equation for the flux density:
	    <div class="equation">
	      $\alpha = \nu(b + 2\nu c) / {\rm S}$
	    </div>
	  </div>
	  <div>
	    We note that the non-logarithmic models may be non-physical, as
	    they allow for negative flux density, but should suffice for how
	    they are used here, as the noise level on observations where
	    they are used is large enough to make it the dominant form of
	    the uncertainty.
	  </div>
	</div>
	<div>
	  <a name="interpreting-vla-information">&nbsp;</a>
	  <h3>VLA Calibrator Information</h3>
	  <div>
	    For those calibrators that are also in the 
	    <a href="https://science.nrao.edu/facilities/vla/observing/callist">
	      VLA calibrator list</a>, the calibrator database page will show
	    the appropriate entry from the
	    <a href="https://science.nrao.edu/facilities/vla/docs/manuals/cal">
	      VLA calibrator manual</a>.
	  </div>
	  <div>
	    The information contained in the calibrator list is very compact, but
	    conveys a significant amount of information. A key to the intepreting
	    the information is given
	    <a href="https://science.nrao.edu/facilities/vla/docs/manuals/cal/list/key">
	      on this page</a>.
	  </div>
	</div>
      </div>

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